Paper contributions.
In the paper, we propose a method to synthesize recurrent neural network (RNN) controllers with exponential stability guarantees for partially observed systems.
We derive a convex inner approximation to the non-convex set of stable RNN parameters based on integral quadratic constraints [1]}, loop transformation [2]} and a sequential semidefinite convexification technique, which guarantees exponential stability for both linear time invariant (LTI) systems and general nonlinear uncertain systems.
A novel framework of projected policy gradient is proposed to maximize some unknown/complex reward function and ensure stability in the online setting where a guaranteed-stable RNN controller is synthesized and iteratively updated while interacting with and controlling the underlying system, which differentiates our works from most post-hoc validation methods.
Finally, we carry out comprehensive comparisons with policy gradient, and demonstrate that our method effectively ensures the closed-loop stability and achieves higher reward on a variety of control tasks, including vehicle lateral control and power system frequency regulation.
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